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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 18 May 2017 15:45:57 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/May/18/t14951187973uau3nbryuz7crx.htm/, Retrieved Fri, 17 May 2024 05:04:50 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 05:04:50 +0200

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.895718	6.9382	0
2	0.796841	6.1723	0
3	0.701859	5.4366	1e-06
4	0.622033	4.8182	5e-06
5	0.499587	3.8698	0.000136
6	0.401623	3.111	0.001427
7	0.311328	2.4115	0.009481
8	0.242467	1.8781	0.032612
9	0.181311	1.4044	0.082673
10	0.141538	1.0963	0.138654
11	0.12331	0.9552	0.171667
12	0.098819	0.7654	0.223503
13	0.002545	0.0197	0.492168
14	-0.080575	-0.6241	0.267453
15	-0.140328	-1.087	0.140698
16	-0.191353	-1.4822	0.071758
17	-0.269151	-2.0848	0.020674

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.895718 & 6.9382 & 0 \tabularnewline
2 & 0.796841 & 6.1723 & 0 \tabularnewline
3 & 0.701859 & 5.4366 & 1e-06 \tabularnewline
4 & 0.622033 & 4.8182 & 5e-06 \tabularnewline
5 & 0.499587 & 3.8698 & 0.000136 \tabularnewline
6 & 0.401623 & 3.111 & 0.001427 \tabularnewline
7 & 0.311328 & 2.4115 & 0.009481 \tabularnewline
8 & 0.242467 & 1.8781 & 0.032612 \tabularnewline
9 & 0.181311 & 1.4044 & 0.082673 \tabularnewline
10 & 0.141538 & 1.0963 & 0.138654 \tabularnewline
11 & 0.12331 & 0.9552 & 0.171667 \tabularnewline
12 & 0.098819 & 0.7654 & 0.223503 \tabularnewline
13 & 0.002545 & 0.0197 & 0.492168 \tabularnewline
14 & -0.080575 & -0.6241 & 0.267453 \tabularnewline
15 & -0.140328 & -1.087 & 0.140698 \tabularnewline
16 & -0.191353 & -1.4822 & 0.071758 \tabularnewline
17 & -0.269151 & -2.0848 & 0.020674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.895718[/C][C]6.9382[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.796841[/C][C]6.1723[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.701859[/C][C]5.4366[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.622033[/C][C]4.8182[/C][C]5e-06[/C][/ROW]
[ROW][C]5[/C][C]0.499587[/C][C]3.8698[/C][C]0.000136[/C][/ROW]
[ROW][C]6[/C][C]0.401623[/C][C]3.111[/C][C]0.001427[/C][/ROW]
[ROW][C]7[/C][C]0.311328[/C][C]2.4115[/C][C]0.009481[/C][/ROW]
[ROW][C]8[/C][C]0.242467[/C][C]1.8781[/C][C]0.032612[/C][/ROW]
[ROW][C]9[/C][C]0.181311[/C][C]1.4044[/C][C]0.082673[/C][/ROW]
[ROW][C]10[/C][C]0.141538[/C][C]1.0963[/C][C]0.138654[/C][/ROW]
[ROW][C]11[/C][C]0.12331[/C][C]0.9552[/C][C]0.171667[/C][/ROW]
[ROW][C]12[/C][C]0.098819[/C][C]0.7654[/C][C]0.223503[/C][/ROW]
[ROW][C]13[/C][C]0.002545[/C][C]0.0197[/C][C]0.492168[/C][/ROW]
[ROW][C]14[/C][C]-0.080575[/C][C]-0.6241[/C][C]0.267453[/C][/ROW]
[ROW][C]15[/C][C]-0.140328[/C][C]-1.087[/C][C]0.140698[/C][/ROW]
[ROW][C]16[/C][C]-0.191353[/C][C]-1.4822[/C][C]0.071758[/C][/ROW]
[ROW][C]17[/C][C]-0.269151[/C][C]-2.0848[/C][C]0.020674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.895718	6.9382	0
2	0.796841	6.1723	0
3	0.701859	5.4366	1e-06
4	0.622033	4.8182	5e-06
5	0.499587	3.8698	0.000136
6	0.401623	3.111	0.001427
7	0.311328	2.4115	0.009481
8	0.242467	1.8781	0.032612
9	0.181311	1.4044	0.082673
10	0.141538	1.0963	0.138654
11	0.12331	0.9552	0.171667
12	0.098819	0.7654	0.223503
13	0.002545	0.0197	0.492168
14	-0.080575	-0.6241	0.267453
15	-0.140328	-1.087	0.140698
16	-0.191353	-1.4822	0.071758
17	-0.269151	-2.0848	0.020674

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.895718	6.9382	0
2	-0.027664	-0.2143	0.415526
3	-0.034687	-0.2687	0.394546
4	0.021887	0.1695	0.432972
5	-0.262279	-2.0316	0.023315
6	0.044585	0.3454	0.365518
7	-0.030186	-0.2338	0.40796
8	0.020023	0.1551	0.438633
9	0.046054	0.3567	0.361273
10	0.020918	0.162	0.435914
11	0.087869	0.6806	0.249363
12	-0.085145	-0.6595	0.256038
13	-0.425885	-3.2989	0.000818
14	-0.036451	-0.2824	0.389323
15	0.012524	0.097	0.461522
16	-0.002259	-0.0175	0.493048
17	-0.017647	-0.1367	0.445867

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.895718 & 6.9382 & 0 \tabularnewline
2 & -0.027664 & -0.2143 & 0.415526 \tabularnewline
3 & -0.034687 & -0.2687 & 0.394546 \tabularnewline
4 & 0.021887 & 0.1695 & 0.432972 \tabularnewline
5 & -0.262279 & -2.0316 & 0.023315 \tabularnewline
6 & 0.044585 & 0.3454 & 0.365518 \tabularnewline
7 & -0.030186 & -0.2338 & 0.40796 \tabularnewline
8 & 0.020023 & 0.1551 & 0.438633 \tabularnewline
9 & 0.046054 & 0.3567 & 0.361273 \tabularnewline
10 & 0.020918 & 0.162 & 0.435914 \tabularnewline
11 & 0.087869 & 0.6806 & 0.249363 \tabularnewline
12 & -0.085145 & -0.6595 & 0.256038 \tabularnewline
13 & -0.425885 & -3.2989 & 0.000818 \tabularnewline
14 & -0.036451 & -0.2824 & 0.389323 \tabularnewline
15 & 0.012524 & 0.097 & 0.461522 \tabularnewline
16 & -0.002259 & -0.0175 & 0.493048 \tabularnewline
17 & -0.017647 & -0.1367 & 0.445867 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.895718[/C][C]6.9382[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.027664[/C][C]-0.2143[/C][C]0.415526[/C][/ROW]
[ROW][C]3[/C][C]-0.034687[/C][C]-0.2687[/C][C]0.394546[/C][/ROW]
[ROW][C]4[/C][C]0.021887[/C][C]0.1695[/C][C]0.432972[/C][/ROW]
[ROW][C]5[/C][C]-0.262279[/C][C]-2.0316[/C][C]0.023315[/C][/ROW]
[ROW][C]6[/C][C]0.044585[/C][C]0.3454[/C][C]0.365518[/C][/ROW]
[ROW][C]7[/C][C]-0.030186[/C][C]-0.2338[/C][C]0.40796[/C][/ROW]
[ROW][C]8[/C][C]0.020023[/C][C]0.1551[/C][C]0.438633[/C][/ROW]
[ROW][C]9[/C][C]0.046054[/C][C]0.3567[/C][C]0.361273[/C][/ROW]
[ROW][C]10[/C][C]0.020918[/C][C]0.162[/C][C]0.435914[/C][/ROW]
[ROW][C]11[/C][C]0.087869[/C][C]0.6806[/C][C]0.249363[/C][/ROW]
[ROW][C]12[/C][C]-0.085145[/C][C]-0.6595[/C][C]0.256038[/C][/ROW]
[ROW][C]13[/C][C]-0.425885[/C][C]-3.2989[/C][C]0.000818[/C][/ROW]
[ROW][C]14[/C][C]-0.036451[/C][C]-0.2824[/C][C]0.389323[/C][/ROW]
[ROW][C]15[/C][C]0.012524[/C][C]0.097[/C][C]0.461522[/C][/ROW]
[ROW][C]16[/C][C]-0.002259[/C][C]-0.0175[/C][C]0.493048[/C][/ROW]
[ROW][C]17[/C][C]-0.017647[/C][C]-0.1367[/C][C]0.445867[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.895718	6.9382	0
2	-0.027664	-0.2143	0.415526
3	-0.034687	-0.2687	0.394546
4	0.021887	0.1695	0.432972
5	-0.262279	-2.0316	0.023315
6	0.044585	0.3454	0.365518
7	-0.030186	-0.2338	0.40796
8	0.020023	0.1551	0.438633
9	0.046054	0.3567	0.361273
10	0.020918	0.162	0.435914
11	0.087869	0.6806	0.249363
12	-0.085145	-0.6595	0.256038
13	-0.425885	-3.2989	0.000818
14	-0.036451	-0.2824	0.389323
15	0.012524	0.097	0.461522
16	-0.002259	-0.0175	0.493048
17	-0.017647	-0.1367	0.445867

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Input Parameters & R Code